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Rate of assimilation of drug in human body

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A drug that has an half life of 20 hours inside the human body and is administered intravenously (I.V.) into a patient. The rate of change of the drug in the body is proportional to the amount present.

Write a differential equation explaining the rate of change of the quantity of the drug and determine the constant proportionality.

The patient receives the drug I.V. at a continuous rate of 4mg/min. Write a differential equation describing the rate of change of the amount of the drug and calculate the solution assuming there is none of the drug initially present in the patient.

It takes 2 hours for the I.V. bag to empty. How much of the drug is in the patient's blood stream at this point.

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Step by step solution provided to help write a differential equation explaining the rate of change of the quantity of a drug, as well as determining the constant proportionality.

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